Convergence of semi-convex functions in CAT(1)-spaces
Abstract We generalize the results of Kuwae–Shioya and Bačák on Mosco convergence established for CAT(0)-spaces to the CAT(1)-setting, so that Mosco convergence implies convergence of resolvents which in turn imply convergence of gradient flows for lower-semicontinuous semi-convex functions. Our techniques utilize weak convergence in CAT(1)-spaces and also cover asymptotic relations of sequences of such spaces introduced by Kuwae-Shioya, including Gromov–Hausdorff limits.
Authors
- Miklós Pálfia (ORCID: https://orcid.org/0000-0003-1164-0081)
- Hedvig Gál
Institutions
- Corvinus University of Budapest (HU)
- University of Szeged (HU)
- HUN-REN Szegedi Biológiai Kutatóközpont (HU)
Publication Details
- Journal
- Calculus of Variations and Partial Differential Equations
- Published
- 2024-09-16
- DOI
- https://doi.org/10.1007/s00526-024-02823-4
- Primary Topic
- Optimization and Variational Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Budapesti Corvinus Egyetem
- Magyar Tudományos Akadémia
- Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
- Nemzeti Kutatási, Fejlesztési és Innovaciós Alap
- National Research, Development and Innovation Office